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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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Question

A1 Let the inner product for polynomial functions on the interval 0 ≤ x ≤ 1 be given by
(f,g) = f* f (x)g(x)r
dx.
(1)
(a) Applying the Gram-Schmidt method to the sequence of powers 1, x, x2, x³,...
find the first three members of the orthonormal basis of polynomials.
(b) Find the best in the mean approximation ao + a1x + a2x² of the function √√x in
the norm defined by the inner product (1).

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